I just figured out the question was about working online rather than finding work online.
I remember him telling me that it was on a military base but the job was for a contractor, one of the big ones like Ratheon tho that may not have been the one.
He was not into scuba but he did say they had good recreation facilities, mainly because of the isolation.
Yes, there's a big base there.
Kwajalein used to be the "target" for ICBM tests. I believe it's the same distance from Vandenberg to Kwaj as from silos in the midwest to the former Soviet Union.
They have missile tracking radars in place to map the precise impact point.
Here's a video of a Minuteman III test: https://www.youtube.com/watch?v=PDL_pIPScSI
You didn't say what kind of teacher, but I know they have contractor staff living there with their families.